Final answer:
The correct equations that represent a system for the given conditions are c. x + y = 37 and d. x - y = 7, which indicate the sum and difference of the two unknown positive numbers. Option C and D are correct.
Step-by-step explanation:
The student is asking for the two equations that represent the system of equations for two unknown positive numbers, x and y, where their sum is 37 and their difference is 7. When two positive numbers are added or subtracted, the results are also positive, according to basic arithmetic rules. In this scenario, the equations representing the sum and difference of x and y can be written as c. x + y = 37 and d. x - y = 7. These two equations satisfy the given conditions for the sum and difference of the two numbers respectively.
To solve the system of equations, one could substitute the value from one equation into the other, or use methods like elimination or graphing. After solving, the student will find the unique values of x and y that satisfy both equations simultaneously.